Should we understand that the electrodes are connected together two by two
My understanding from the links is that 1 wire pair serves for DC bias to vary the EM field inside the dielectric material and the changing capacitance can be utilized between the other wire pair. (So I suppose that the four wires are electrically isolated from each other.) I base this on this quote from the wiki link I gave: The dielectric permittivity of such material changes significantly with variations in the strength of the electric field in which it is located. As the voltage increases, the dielectric constant (and therefore the capacitance of the capacitor) rises to a certain value and then decreases. ...
If the control voltage can be applied independently of the signal
I don't know. Probably a fool...